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On the concept of dynamical reduction: the case of coupled oscillators

裕也 中尾, Hiroya Nakao

Published Dec 1, 2019• 0 citations
OpenAlex

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The quantum mechanical concept of an ”atom in a molecule" is synthetically emulated and analyzed in the form of a nonlinear electronic circuit. The circuit is comprised of coupled quantized oscillators. Quantized oscillators are novel and not generally known. Such systems are shown to be consistent with quantum chemical dynamics. Such a network of quantized oscillators achieves equilibriums that are consistent with naturally occurring molecules. These capabilities offer an alternative to von Neumann digital based computations, whereby solutions to complex systems are determined as equilibriums, as is the case of nature. Historically, quantized solutions have been associated with solutions to Shrödinger’s Equation. Shrödinger Equation based observations are typically rendered, if possible, by numerical calculations. By comparison, the approach presented in this work relies on synthesizing quantized electronic devices, which are novel, in order to achieve dynamical interactions consistent with naturally occurring ones. Detailed dynamics based on actual devices are provided. The theoretical underpinnings are described. This topic has broad implications for a variety of concepts associated with quantum mechanics, including computations and entanglement, as well as various oscillator circuits of fundamental importance.
Employing the fermionic and bosonic Hamiltonians for the collective oscillator linearly FC-coupled with several heat baths, the analytical expressions for the collective occupation number are derived within the non-Markovian quantum Langevin approach. The master equations for the occupation number of collective subsystem are derived and discussed. In the case of Ohmic dissipation with Lorenzian cutoffs, the possibility of reduction of the system with several heat baths to the system with one heat bath is analytically demonstrated. For the fermionic and bosonic systems, a comparative analysis is performed between the collective subsystem coupled to two heat baths and the reference case of the subsystem coupled to one bath.